About LaTeX display error

[Noctiro]

Scaling Issues

1. The \left and \right commands do not automatically adjust the size of symbols.
2. The square root \sqrt does not scale properly.
3. In the cases environment, the equals sign is not aligned properly.

\begin{align}
A\sin\alpha + B\cos\alpha  & = \sqrt{A^2+B^2}\left(\sin\alpha \cdot \frac{A}{\sqrt{A^2+B^2}} + \cos\alpha \cdot \frac{B}{\sqrt{A^2+B^2}}\right) \\
& = \sqrt{A^2+B^2}(\sin\alpha \cdot \cos\varphi + \cos\alpha \cdot \sin\varphi) \\
& = \sqrt{A^2+B^2}\sin(\alpha + \varphi)
\end{align}

Alignment Issues

1. The horizontal line above \overline{abc} does not cover the entire expression.
   

2. The left and right parentheses do not align properly.

3. The curly braces are not aligned properly.

a_{n} =
\begin{cases}
a_{1} \cdot q^{n-1} \\
a_{m} \cdot q^{n-m}
\end{cases}

Layout Issues

1. Layout issues—sometimes multi-line formulas appear too crowded.